Textbook Question
Find each product. (x+5)(x−5)
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Ch. P - Fundamental Concepts of Algebra
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
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Table of contents
- Ch. P - Fundamental Concepts of Algebra311
- Ch. 1 - Equations and Inequalities398
- Ch. 2 - Functions and Graphs407
- Ch. 3 - Polynomial and Rational Functions306
- Ch. 4 - Exponential and Logarithmic Functions247
- Ch. 5 - Systems of Equations and Inequalities173
- Ch. 6 - Matrices and Determinants143
- Ch. 7 - Conic Sections124
- Ch. 8 - Sequences, Induction, and Probability251
Chapter 1, Problem 31
Find the union of the sets. {1,3,5,7}∪{2,4,6,8,10}
Verified step by step guidance1
Identify the two sets given: the first set is \(\{1,3,5,7\}\) and the second set is \(\{2,4,6,8,10\}\).
Recall that the union of two sets, denoted by \(\cup\), combines all elements from both sets without repeating any elements.
List all elements from the first set: \$1, 3, 5, 7$.
Add all elements from the second set: \$2, 4, 6, 8, 10$, making sure not to repeat any elements already listed.
Write the union set by combining all unique elements from both sets into one set.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Set Union
The union of two sets combines all unique elements from both sets into one set. It is denoted by the symbol ∪. For example, if A = {1, 2} and B = {2, 3}, then A ∪ B = {1, 2, 3}.
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Set Notation
Set notation uses curly braces {} to list elements of a set. Elements are separated by commas, and each element is unique within the set. Understanding this notation helps in identifying and manipulating sets.
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Distinct Elements in Sets
When forming unions, repeated elements are only listed once. Recognizing that sets do not include duplicates ensures the union contains each element a single time, regardless of how many times it appears in the original sets.
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Related Practice
Textbook Question
In Exercises 15–58, find each product. (7x3+5)(x2−2)
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Textbook Question
Use the quotient rule to simplify the expressions in Exercises 23–32. Assume that x > 0. √24x^4/√3x
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Textbook Question
Use the quotient rule to simplify the expressions in Exercises 23–32. Assume that x > 0. √500x3/√10x-1
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Textbook Question
Simplify each exponential expression in Exercises 23–64.
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Textbook Question
In Exercises 15–32, multiply or divide as indicated. (x2−4)/(x2+3x−10) ÷ (x2+5x+6)/(x2+8x+15)
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